Blender Python: Call operator function from another function?
You can pass what you want and even self, this way it is easy determine where the call is coming from. Operator based on Templates > Python > Operator Simple:

import bpy


def main(operator, context):
    print (operator, context)
    operator.report({'INFO'}, 'Call is comming from: {}'.format(operator))
    #return operator


class SimpleOperator(bpy.types.Operator):
    """Tooltip"""
    bl_idname = "object.simple_operator"
    bl_label = "Simple Object Operator"

    @classmethod
    def poll(cls, context):
        return context.active_object is not None

    def execute(self, context):
        main(self, context)
        return {'FINISHED'}


def register():
    bpy.utils.register_class(SimpleOperator)


def unregister():
    bpy.utils.unregister_class(SimpleOperator)


if __name__ == "__main__":
    register()

    # test call
    bpy.ops.object.simple_operator()